Transboundary Extremal Length

  title={Transboundary Extremal Length},
  author={O. Schramm},
We introduce two basic notions, `transboundary extremal length' and`fat sets', and apply these concepts to the theory of conformal uniformization of multiply connected planar domains. A new short proof is given to Koebe's conjecture in the countable case: every planar domain with countably many boundary components is conformally equivalent to a circle domain. This theorem is further generalized in two directions. We show that the same statement is true for a wide class of domains with… CONTINUE READING

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